Space Time Units

Submitted by bperet on Sun, 08/10/2008 - 01:24

The following table defines the aspects and powers of units of space and time commonly associated with mechanical, electrical and other phenomenon.

Mechanical

#Dims		Local (speed)				Non-Local (energy)
a	b	(s^a/t^b)		(s^b/t^a)		Conjugate (t^a/s^b)		Inverse (t^b/s^a)
0	0	Unit Speed spatial progression				Unit Speed temporal rotational base
0	1	1/t	angular velocity (ω)	s	length (d)	1/s		t	duration (s)
0	2	1/t²		s²	area (A)	1/s²		t²
0	3	1/t³		s³	volume	1/s³		t³
1	1	s/t	speed (v)			t/s	torque (L), energy (E), work (W)
1	2	s/t²	acceleration (a)	s²/t		t/s²	force (F)	t²/s
1	3	s/t³		s³/t		t/s³		t³/s	moment of inertia (I)
1	4	s/t⁴		s⁴/t		t/s⁴	pressure	t⁴/s
2	2	s²/t²	c²			t²/s²	momentum
3	3	s³/t³	gravity			t³/s³	mass

#Dims		Local (speed)				Non-Local (energy)
a	b	(s^a/t^b)		(s^b/t^a)		Conjugate (t^a/s^b)		Inverse (t^b/s^a)
0	1	1/t		s/1	electric quantity (q*) capacitance (C)	1/s	power (watts)	t/1	dipole moment
1	1	s/t	current (ampere) voltage (statvolts)			t/s	electric charge (Q*) current (statamps)
1	2	s/t²		s²/t	permittivity (ε)	t/s²	voltage (volts)	t²/s
1	3	s/t³		s³/t		t/s³	electric field intensity (E)	t³/s
2	2	s²/t²	conductivity resistance (statohms)			t²/s²	Resistivity
2	3	s²/t³		s³/t²		t²/s³	resistance (ohms)	t³/s²

* "q" is considered the same as "Q" (charge) in conventional science

#Dims		Local (speed)		Non-Local (energy)
a	b	(s^a/t^b)	(s^b/t^a)	Conjugate (t^a/s^b)		Inverse (t^b/s^a)
1	2	s/t²	s²/t	t/s²		t²/s	dipole moment
2	2	s²/t²		t²/s²	magnetic charge (*) pole strength (weber) magnetic flux
2	3	s²/t³	s³/t²	t²/s³	magnetic vector potential (gilbert) magnetomotive force (MMF)	t³/s²
2	4	s²/t⁴	s⁴/t²	t²/s⁴	magnetic field intensity (oersted)	t⁴/s²
3	3	s³/t³		t³/s³	inductance
3	4	s³/t⁴	s⁴/t³	t³/s⁴	permeability (µ)	t⁴/s³

** Magnetic charge is not recognized.